Galois’ Dream: Group Theory and Differential Equations by Kuga

introduction

• ‘Galois’ Dream: Group Theory and Differential Equations by Michio Kuga
• 정규특이점을 가지는 이계선형미분방정식, 즉 이계 Fuchsian 미분방정식의 해가 언제 리우빌 확장의 원소가 되는지 모노드로미군을 통해 할 수 있는 이야기를 펼쳐보인다.

주요내용

excepts from the preface

(i) It can serve as an introduction to algebraic systems (groups), topology and analysis (function theory)

(ii)Only elementary knowledge of these three subjects is needed, but all three are necessary. This theory is the most primitive example that the intersection of many different disciplines is the most interesting mahtematics. It can help convince students that mathematics is a unity; it also gives a wider perspective of mathematics

(iii)It gives a geometric understanding of Galois theory

(iv)There are many challenging problems which are not too difficult for student exercises.

(v)Above all, I cannot forget the old dogma that the most interesting aspect of analysis is its algebraic structure.

review

• Galois' Dream—Group Theory and Differential Equations (Michio Kuga)
  • Jeremy J. Gray, SIAM Rev. Volume 36, Issue 1, pp. 126-126 (March 1994)

관련항목

• differential Galois theory

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위키데이터

• ID : Q6837920

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• [{'LOWER': 'michio'}, {'LEMMA': 'Kuga'}]